An angle measure of 630 degrees was written in radians as \(x\pi\). What is the value of \(x\)?

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A circle is \(360\degree\) or \(2\pi\) radians. We use can a simple proportion to find the correct number of radians.

$$ \frac{2\pi \text{ radians}}{360\degree} = \frac{R \text{ radians}}{630\degree} $$ $$ 2\pi \cdot 630 = 360 \cdot R $$ $$ 1260=360R $$ $$ \frac{1260\pi}{360}=R $$ $$ 3.5\pi=R $$ $$ R= \boxed{\frac{7}{2}}\pi $$

We can do unit conversions as long as we know the conversion, \(\pi\text{ radians}=180\degree\).

$$ 630 \degree \cdot \frac{\pi \text{ radians}}{180 \degree} $$ $$ 630\cdot \frac{\pi}{180} \text{ radians}$$ $$ =\frac{63}{18}\pi $$ $$ = \frac{21}{6}\pi $$ $$ = \boxed{\frac{7}{2}}\pi $$